Determine if the function is continuous to its domain
1 answer:
Yes, it is continuous to its domain
<h2>Explanation:</h2><h2></h2>In order to find the domain of the function we need to get the restrictions:
1. From natural log:
2. From quotient:
Matching these two restrictions the domain is:
So the function is continuous to its domain because is defined for every x-value in the interval )
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... L(x) = f'(1)(x -1) +f(1)
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so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
